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Research Interests
Research Interests
Broadly, I am interested in reduced order modeling, where one uses information about a large-scale dynamical system to find a much smaller system that well approximates the input-output mapping of the original system. This smaller system can then be simulated for a much smaller computational cost. The "information" used to construct such models can be an internal description of the system, or various types of input-output data.
Of particular interest to me is the case where one cannot assume to have an internal description of the system, but must construct reduced order models directly from data. Constructing such models poses intriguing numerical challenges, and much of my work thus far has been in tackling these challenges.
Learning frequency input-output data from purely time-domain data
Learning frequency input-output data from purely time-domain data
When constructing reduced order models from input-output data, one can choose to work with information in the frequency domain or time domain. Frequency domain techniques have many attractive properties, including bounds on the mismatch between the outputs of the reduced and true system for any input. Unfortunately, frequency information can at times be costly or impossible to obtain.
My work provides a numerically robust implementation of a method to learn frequency information from time domain data. This work enables the powerful tools of frequency-based reduced order modeling to be used in the case where only time-domain data is available.
An arXiv preprint is available, as well as the MatLab code.
Learning Optimal Reduced Order Models from Purely Time-Domain Data
Learning Optimal Reduced Order Models from Purely Time-Domain Data
Finding reduced order models that are optimal in an appropriate sense has classically required access to a realization of the full order model. The Transfer Function Iterative Rational Krylov Algorithm (TF-IRKA) constructs optimal ROMs from frequency data, but in some practical scenarios, this information may be difficult or impossible to obtain.
While my previous work provided much-needed computational improvements to the process of extracting frequency information from time-domain data, constructing optimal models introduced new challenges. In this work, we provide the necessary analysis to produce optimal reduced order models directly from a single time-domain simulation of the full-order model.
An arXiv preprint is available, as well as the MatLab code.
Learning Structured Dynamical Systems from data
Learning Structured Dynamical Systems from data
Data-driven reduced order modeling is a tool to construct models of physical phenomena when access to governing equations or a state-space model is not possible, but input-output data is abundant. While there are many available methods capable of producing models that fit the given data to high accuracy, such methods typically do not preserve underlying differential structures which are important for interpretation of the models. A common structure to appear in mechanical systems is an explicit dependence on the second time derivative. Inspired by the popular Adaptive Anderson-Antoulas (AAA) algorithm, we develop a structure-preserving second-order AAA algorithm that is capable of learning highly accurate second-order surrogate models from frequency response measurements.
An arXiv preprint and associated code will be available soon!
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